A381278 Expansion of e.g.f. exp(sin(3*x) / 3).

1, 1, 1, -8, -35, -8, 1117, 6328, -19943, -513728, -2096711, 30574720, 447401845, 23791744, -59033858219, -527680180736, 4971322421425, 144677554315264, 430091284739185, -27641200139694080, -398305237630617971, 2876369985206861824, 145441158283475935309

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-9)^k * binomial(n-1,2*k) * a(n-2*k-1).

a(n) = Sum_{k=0..n} (3*i)^(n-k) * A136630(n,k), where i is the imaginary unit.

Prog

(PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (3*I)^(n-k)*a136630(n, k));

Crossrefs

Cf. A002017, A009210.

Cf. A136630, A352640, A381286.

Sequence in context: A318244 A280395 A158991 * A265161 A303805 A360658

Adjacent sequences: A381275 A381276 A381277 * A381279 A381280 A381281

Keyword

sign

Author

Seiichi Manyama, Feb 18 2025

Status

approved